Abstract:
In spreading processes, droplets containing surfactant form complex fingering phenomena. Based on the lubrication theory, FreeFem++ was used to numerically solve the 2D evolution equations of the film thickness and surfactant concentration on the uneven substrates to obtain the nonlinear characteristics of fingering. The evolution of the film thickness and disturbance energy under different substrates were analyzed, and the splitting and shielding phenomena of fingers were examined using fractal dimension and the variance of fingers. The results show that for substrates with the same morphology, the increase of the roughness of the substrate enhances the disturbance intensity and the substrate roughness is positively correlated with the disturbance energy of the ultra-thin liquid film area. The roughness and the crossflow of substrates affect the fractal dimension of fingers and with the same roughness, only the 1D groove substrate promotes the disturbance. Compared with the groove substrates, the corrugated substrates are more sensitive to roughness, and their disturbance energy changes more drastically with the roughness. Increasing the change of substrates along the y direction accelerates the splitting of fingers, while increasing the roughness of substrates strengthens the shielding of fingers.